LiDAR sensors provide rich 3D information about their surroundings and are becoming increasingly important for autonomous vehicles tasks such as localization, semantic segmentation, object detection, and tracking. Simulation accelerates the testing, validation, and deployment of autonomous vehicles while also reducing cost and eliminating the risks of testing in real-world scenarios. We address the problem of high-fidelity LiDAR simulation and present a pipeline that leverages real-world point clouds acquired by mobile mapping systems. Point-based geometry representations, more specifically splats (2D oriented disks with normals), have proven their ability to accurately model the underlying surface in large point clouds, mainly with uniform density. We introduce an adaptive splat generation method that accurately models the underlying 3D geometry to handle real-world point clouds with variable densities, especially for thin structures. Moreover, we introduce a fast LiDAR sensor simulator, working in the splatted model, that leverages the GPU parallel architecture with an acceleration structure while focusing on efficiently handling large point clouds. We test our LiDAR simulation in real-world conditions, showing qualitative and quantitative results compared to basic splatting and meshing techniques, demonstrating the interest of our modeling technique.